Question

What number is the answer for number 4 and why?

Answer 1

The easiest way to solve this problem is to multiply the second term by -1/-1, obtaining the following expression:

$\frac{3y}{2y-6}+\frac{9}{6-2y}\cdot\frac{-1}{-1}=\frac{3y}{2y-6}-\frac{9}{2y-6}$

Now, we can solve the substraction of homogeneous fractions:

$\frac{3y}{2y-6}-\frac{9}{2y-6}=\frac{3y-9}{2y-6}=\frac{3(y-3)}{2(y-3)}=\frac{3}{2}$

The answer is 3/2.